# Activities

• • • ##### Subject Area

• Math: Statistics: Inferential Statistics

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 7 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

## Probability as Relative Frequency

#### Activity Overview

In this activity, students use simulation to justify the concept of the Law of Large Numbers. They understand that as the sample size increases, the relative frequency of which an event occurs approaches the probability of that event happening. Students investigate the binomial and geometric probability functions, and determine the mean and standard deviation.

#### Before the Activity

Install the Statistics with List Editor application on the calculator using one of these two methods:

• TI Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable
• TI-Navigator™ "send to class" feature
• See the attached PDF file for detailed instructions for this activity
• Print pages 95 - 108 from the attached PDF file for your class

#### During the Activity

Distribute the pages to the class.

Law of Large Numbers:

• A player has a batting average of 0.333
• Simulate the at-bat event as a toss of die and consider only 1, 2, or 3 spots
• Find the cumulative success rate after 6 trials and 150 trials
• Create a dotplot to view the data graphically
• Note that as the sample size increases, the mean of the sample approaches the batting average of 0.333 (population mean)

• Binomial Distribution:
• Enter the number of trials, success probability, and the number of successful events
• Determine the success rate of the event happening
• Calculate the mean and the standard deviation for the binomial distribution
• Set up a probability histogram and examine the center and spread
• Simulate trials of the event and calculate the number of successes for each trial

• Geometric Distribution:
• Determine the probability of an event happening in a particular trial
• Repeat the step for at least 50 trials
• Enter the geometric distribution probabilities as a list
• Determine the mean and set up a probability histogram
• Simulate the first 10 trials and determine the trial in which the event first succeeded
• Continue for 100 trials to obtain a better estimate
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary